Flexural plate wave sensor

ABSTRACT

A method for manufacturing a flexural plate wave sensor, the method including the steps of depositing an etch-stop layer over a substrate, depositing a membrane layer over said etch stop layer, depositing a piezoelectric layer over said membrane layer, forming a comb pattern with drive teeth which span across an entire length of the piezoelectric layer on said piezoelectric layer, etching a cavity through the substrate, the cavity having substantially parallel interior walls, and removing a portion of the etch stop layer between the cavity and the membrane layer to expose a portion of the membrane layer.

RELATED APPLICATIONS

This application is a Divisional application of U.S. patent applicationSer. No. 10/675,398, filed on Sep. 30, 2003, hereby incorporated byreference herein.

FIELD OF THE INVENTION

This invention relates generally to flexure plate wave sensors and moreparticularly to an improved comb pattern for a flexural plate wavesensor.

BACKGROUND OF THE INVENTION

A flexural plate wave (FPW) sensor includes a diaphragm or plate whichis driven so it oscillates at frequencies determined by a comb patternand the flexural plate geometry. The comb pattern is disposed over theflexural plate and establishes electric fields which interact with theplate's piezoelectric properties to excite motion. The eigenmodesdescribe the diaphragm displacements which exhibit spatially distributedpeaks. Each eigenmode consists of n half sine periods along thediaphragm's length. A typical FPW sensor can be excited to eighty ormore eigenmodes. In a typical FPW eigenmode, the plate deflectionconsists of many sinusoidal (or nearly sinusoidal) peaks.

Prior art flexure plate wave sensors typically include drive combs atone end of the plate and sense combs at the other end. The drive combsof these prior art devices typically cover only twenty-five to fortypercent of the total length of the plate. When the number of drive teethis small compared to the number of eigenmodes peaks, the small number ofdrive teeth can align with several eigenmodes. The result is that notonly are the eigenmodes perfectly aligned with the comb teeth excited,but other eigenmodes are also excited. In signal processing and spectralanalysis, this effect is known as leakage. A significant drawback ofprior designs is that the increased number of eigenmodes excited in theFPW sensor produces a series of resonance peaks of similar amplitude andirregular phase which increases design complexity and the operation ofthe prior art flexure plate wave sensors.

Moreover, prior art flexural plate wave sensors utilize drive and sensecombs at opposite ends of the flexural plate and rely on analysis basedon an analogy to surface acoustic waves (SAW) wherein the wavespropagate away from the drive combs and toward the sense combs and backreflections are regarded as interference. A distinct disadvantage ofthis analysis is that SAW theory does not account for numerous smallpeaks produced by the sensor resulting in calculated gains (e.g., peaksof similar magnitude) which are low and do not account for sharp phasedrops seen with the peaks (e.g., irregular phase).

SUMMARY OF THE INVENTION

It is therefore an object of this invention to provide an improvedflexural plate wave sensor.

It is a further object of this invention to provide such a sensor whichreduces the number of eigenmodes excited in the flexural plate.

It is a further object of this invention to provide such a sensor whichoutputs a single pronounced peak, or a peak much larger than any of theother peaks.

It is a further object of this invention to provide such a sensor whichoutputs a distinct phase.

It is a further object of this invention to provide such a sensor whichsimplifies the operation and design of the sensor.

It is a further object of this invention to provide such a sensor whichimproves stability and performance of the sensor.

It is a further object of this invention to provide such a sensor whichimproves stability by eliminating erroneous readings due to interferencecreated by mode hopping from other eigenmodes is eliminated.

This invention results from the realization that a truly effective androbust flexural plate wave sensor is achieved by utilizing a unique combpattern over the flexural plate with drive teeth disposed across theentire length of the flexural plate and which, in one embodiment, arealigned with all the eigenmodes of the flexural plate resulting in theability to reduce the number of eigenmodes excited in the plate and theoutput of a single pronounced peak with a distinct phase simplifying theoperation and design of the flexural plate wave sensor.

This invention features a flexural plate wave sensor including aflexural plate having a length and a width, and a comb pattern over theflexural plate with drive teeth disposed across the entire length of theflexural plate to reduce the number of eigenmodes excited in the plateand thereby simplifying the operation and design of the flexure platewave sensor. The sensor may include sense teeth disposed across theentire length of the flexure plate interleaved with the drive teeth. Inone example, the sense teeth face in one direction and the drive teethface in an opposite direction.

In one embodiment of this invention, the comb pattern is aligned withone eigenmode of the flexural plate thereby exciting one eigenmode inthe plate. In one design, the comb pattern allows the sensor to output asingle pronounced peak thereby improving the performance of the sensor.The comb pattern of this invention may also reduce a transfer functionof the sensor to a single peak, or a peak much larger than any otherpeak. In one preferred embodiment, the drive teeth are aligned with theeigenmodes excited in the flexural plate. The sense teeth may also bealigned with the eigenmodes excited in the flexural plate. Typically,the comb pattern provides for establishing electric fields whichinteract with piezoelectric properties of the flexural plate to excitemotion. The comb pattern may be made of a material chosen from the groupconsisting of copper, titanium-platinum-gold (TiPtAu) metal,titanium-platinum (TiPt), and aluminum. Typically, the comb pattern isapproximately 0.1 μm thick and may include wire bond pad areas andground contacts. In one design, the drive teeth are on the flexuralplate. The sense teeth may also be on the flexural plate. Ideally, thedrive teeth span across an entirety of the width of the flexural plate.The sense teeth may also span across an entirety of the width of theflexural plate.

The flexure plate wave sensor may include a base substrate, an etch stoplayer disposed over the base substrate, a membrane layer disposed overthe etch stop layer, a cavity disposed in the base substrate and theetch stop layer, thereby exposing a portion of the membrane layer, thecavity having substantially parallel interior walls, a piezoelectriclayer disposed over the membrane layer and the comb pattern disposedover the piezoelectric layer. The piezoelectric layer may be formed froma material selected from the group consisting of aluminum nitrite, zincoxide and lead zirconium titanate. The etch stop layer is typicallyformed from silicon dioxide. Ideally, the membrane layer is formed fromsilicon. In one example, the base substrate is formed from silicon.

In one design of this invention, the base substrate includes asilicon-on-insolator (SOI) wafer, which may include an upper surface ofsilicon forming the membrane layer bonded to an etch stop layer. Inother examples, the piezoelectric transducer may be deposited over theupper surface of the epitaxial silicon. Ideally, grounding contacts tothe epitaxial silicon are provided by etching an opening into thepiezoelectric transducer. In one design, the comb pattern includestitanium-platinum-gold (TiPtAu) metal. The comb pattern typicallyincludes interdigital metal electrodes, wire bond pad areas, and groundcontacts. In an embodiment, the base substrate is approximately 380 μmthick, the upper epitaxial surface is approximately 2 μm thick, thelayer of SiO₂ is approximately 1 μm thick, and the comb pattern isapproximately 0.1 μm thick. The drive teeth may be approximately 300 to2000 μm in length and the spacing between the drive teeth may beapproximately 25 to 50 μm. Typically, the sense teeth are approximately300 to 2000 μm in length and the spacing between the sense teeth isapproximately 25 to 50 μm.

This invention further features a flexural plate wave sensor including aflexural plate having a length and a width, and a comb pattern over theflexural plate with drive and sense teeth disposed across the entirelength of the flexural plate to reduce the number of eigenmodes excitedin the plate and thereby simplifying the operation and design of theflexure plate wave sensor.

This invention also features a flexural plate wave sensor including aflexural plate having a length and a width, and a comb pattern over theflexural plate with first and second sets of drive teeth disposed acrossthe entire length of the flexural plate to reduce the number ofeigenmodes excited in the plate and thereby simplify the operation anddesign of the flexural plate wave sensor. In one embodiment the sensorincludes first and second sets of sense teeth disposed across the entirelength of the flexural plate. The first and second sets of drive teethtypically face in opposite directions. The first and second sets ofsense teeth may face in opposite directions. In one design, the firstand second sets of drive teeth are interleaved. The first and secondsets of sense teeth may also be interleaved. The first and second setsof interleaved drive teeth may span the entire length and approximatelyfifty percent of the width of the flexural plate. The first and secondsets of interleaved sense teeth may also span the entire length andapproximately fifty percent of the width of the flexural plate.Typically, the first and second sets of drive teeth face in the samedirection, and the first and second sets of sense teeth face in the samedirection. In one embodiment, the first set of drive teeth isinterleaved with the first set of sense teeth. The first set of driveteeth interleaved with the second set of sense teeth together may spanapproximately fifty percent of the width of the flexural plate. Thesecond set of drive teeth may be interleaved with the second set ofsense teeth. In other designs, the second set of drive teeth interleavedwith the first set of sense teeth together may span approximately fiftypercent of the width of the flexural wave plate.

This invention further features a flexural wave plate sensor including aflexural plate having a length and a width, and a comb pattern over theflexural plate with first and second sets of drive teeth disposed overthe flexural plate. Typically, the first set of drive teeth spanapproximately seventy-five percent of the length of the flexural plateand the second set of drive teeth span approximately twenty-five percentof the length of the flexural plate. The comb pattern reduces the numberof eigenmodes excited in the plate and thereby simplifying the operationand design of the flexural plate wave sensor.

In one embodiment, the sensor may include first and second sets of senseteeth disposed over the flexural plate, the first set of sense teethspanning approximately seventy-five percent of the length of theflexural plate and the second set of sense teeth spanning approximatelytwenty-five percent of the length of the flexural plate. The first andsecond sets of sense teeth may be interleaved with the first and secondsets of drive teeth. In one example, the first and second sets of driveteeth face one direction and the first and second sense teeth face in anopposite direction.

In other designs, the flexural plate wave sensor may include a flexuralplate having a length, width, and a center, and a comb pattern over theflexural plate with first and second sets of drive teeth disposed acrossapproximately fifty percent of the length of the flexural plate, eachset of drive teeth spanning approximately an entirety of the width ofthe flexural plate at one end and curving toward the center of theflexural plate at approximately the center of the plate. Ideally, thecomb pattern reduces the number of eigenmodes excited in the plate andthereby simplifying the operation and design of the flexural plate wavesensor. The sensor may also include first and second sets of sense teethdisposed across approximately fifty percent of the length of theflexural plate, each set of sense teeth spanning approximately anentirety of the width of the flexural plate and curving toward thecenter of the flexural plate at approximately a middle of the plate.

This invention also features a flexural wave plate sensor including aflexural plate having a length and a width, and a comb pattern over theflexural plate. The comb pattern may include drive teeth and sense teethdisposed over the flexural plate. The drive teeth may span approximatelyfifty percent of the length of the flexural plate. The sense teeth mayspan approximately the fifty percent of the length of the flexuralplate. Ideally, the comb pattern reduces the number of eigenmodesexcited in the plate and thereby simplifying the operation and design ofthe flexural plate wave sensor.

This invention further features a flexural wave plate sensor with aflexural plate having a length and a width, and a comb pattern over theflexural plate. The comb pattern may include a set of drive teeth and aset of sense teeth. The set of drive teeth and the set of sense teethmay be disposed over the flexural plate. The drive teeth may spanapproximately fifty percent of the length of the flexural plate, and thesense teeth may span approximately fifty percent of the length of theflexural plate. Ideally, the comb pattern reduces the number ofeigenmodes excited in the plate and thereby simplifying the operationand design of the flexural plate wave sensor.

This invention also features a method for manufacturing a flexural platewave sensor, the method including the steps of depositing an etch-stoplayer over a substrate, depositing a membrane layer over the etch stoplayer, depositing a piezoelectric layer over the membrane layer, forminga comb pattern with drive teeth which span across an entire length ofthe piezoelectric layer on the piezoelectric layer, etching a cavitythrough the substrate, the cavity having substantially parallel interiorwalls, and removing a portion of the etch stop layer between the cavityand the membrane layer to expose a portion of the membrane layer. Themethod of the manufacturing of a flexural plate wave sensor of thisinvention may further include the steps of etching a hole in thepiezoelectric and forming a ground contact on the silicon membranelayer.

This invention further features a method for manufacturing a flexuralplate wave sensor, the method including the steps of depositing anetch-stop layer over a substrate, depositing a membrane layer over theetch stop layer, depositing a piezoelectric layer over the membranelayer, forming a comb pattern on the piezoelectric layer, the combpattern including drive and sense teeth which span an entire length ofthe membrane layer, forming a second transducer on the piezoelectriclayer, spaced from the first transducer, etching a cavity through thesubstrate, the cavity having substantially parallel interior walls,removing the portion of the etch stop layer between the cavity and themembrane layer to expose a portion of the membrane layer, and depositingan absorptive coating on the exposed portion of the membrane layer.

The method of manufacturing a flexural plate of this invention mayfurther include the steps of etching a hole in the piezoelectric andforming a ground contact on the silicon membrane layer.

BRIEF DESCRIPTION OF THE DRAWINGS

Other objects, features and advantages will occur to those skilled inthe art from the following description of a preferred embodiment and theaccompanying drawings, in which:

FIG. 1 is a schematic top view of a prior art flexural plate wave sensorshowing drive and sense combs extending over approximately twenty-fiveto forty percent of the flexural wave plate;

FIG. 2 is a graph showing the relationship of eigenmodes displacementsto drive teeth for the sensor shown in FIG. 1;

FIG. 3A is a graph showing the typical output for the wave sensor shownin FIG. 1;

FIG. 3B is a graph showing the irregular phase response for the peaksshown in FIG. 3A;

FIG. 4 is a schematic side view showing the direction of wavepropagation of the sensor shown in FIG. 1;

FIG. 5 is a schematic top view of one embodiment of the flexural platewave sensor in accordance with the subject invention;

FIG. 6A is a graph showing a single pronounced peak output by theflexural plate wave sensor shown in FIG. 5;

FIG. 6B is a graph showing a distinct phase response for the peak shownin FIG. 6A;

FIG. 7A is another graph showing several pronounced peaks of variousmagnitude output by the flexural plate wave sensor shown in FIG. 5;

FIG. 7B is a graph showing a distinct phase response for the peaks shownin FIG. 7A;

FIG. 8 is a schematic side view showing the various layers of theflexural plate wave sensor of this invention;

FIG. 9 is a schematic top view of another embodiment of the comb patternof the flexural plate wave sensor of this invention;

FIG. 10 is a schematic top view of another example of a comb pattern forthe flexural plate wave sensor of this invention;

FIG. 11A is a schematic top view of another design of the comb patternof the flexural plate wave sensor of this invention;

FIG. 11B is a schematic top view of another design of the comb patternof the flexural plate wave sensor of this invention;

FIG. 12 is a schematic top view of yet another design of the combpattern of the flexural plate wave sensor of this invention;

FIG. 13 is a flowchart showing the primary steps associated with onemethod of manufacturing a flexural plate wave sensor in accordance withthis invention;

FIG. 14 is a schematic diagram of the circuitry associated with oneembodiment of the flexural plate wave sensor in accordance with thesubject invention;

FIGS. 15A-15C are graphs showing several examples of the output of theflexural plate wave sensor of the subject invention;

FIGS. 16A-16F are a listing of the MATLAB® code for a three-modefrequency response of one embodiment of the flexural plate wave sensorof this invention;

FIG. 17 is a graph showing the relative eigenfrequencies of oneembodiment of the flexural plate wave sensor of this invention; and

FIG. 18 is a graph showing the static plate deflections for a sinusoidalload on the flexural plate wave sensor of this invention.

DISCLOSURE OF THE PREFERRED EMBODIMENT

Aside from the preferred embodiment or embodiments disclosed below, thisinvention is capable of other embodiments and of being practiced orbeing carried out in various ways. Thus, it is to be understood that theinvention is not limited in its application to the details ofconstruction and the arrangements of components set forth in thefollowing description or illustrated in the drawings.

As discussed in the Background section above, prior art flexure platewave sensor 10, FIG. 1 includes drive comb 14 with drive teeth 16 and 18and drive comb 20 with drive teeth 22 and 24. Typically, drive combs 14and 20 are driven at opposite polarity, e.g., drive comb 14 is driven ata positive polarity and drive comb 20 is driven at a negative polarity,to align with the positive and negative peaks of the eigenmodes.

As shown in FIG. 1, drive combs 14 and 20 are disposed over onlyapproximately twenty-five to forty percent of the entire length offlexural plate 38. Because of the limited length extent of drive combs14 and 20, there is a limited number of drive teeth, e.g., drive teeth16, 18, 22, and 24. As discussed in the Background section above, whenthe number of drive teeth is small compared to the number of eigenmodepeaks of the flexural plate 38, several eigenmodes will be excited.

For example, FIG. 2 shows the modal displacement for longitudinaleigenmodes, with n=20 and n=21, (where n=mode number≅½ sine periods) offlexural plate 38 shown in FIG. 1. As shown in FIG. 2, there is limitednumber of drive teeth 16, 18, 22, and 24 relative to the number ofeigenmodes peaks 39 and 41. The result is that not only are the n=20eigenmodes perfectly aligned with the drive teeth 16, 18, 22, and 24excited, but other eigenmodes are also excited, as shown by arrows 43,45, 49, and 51. The increased number of eigenmodes excited produces aseries of resonance peaks of similar amplitude as shown by peaks 60, 62,64 and 66, FIG. 3A, and irregular phase, as shown in FIG. 3B. The resultis increased complexity in the electronic design and operation of priorart flexural plate wave sensor 10.

Prior art sensor 10, FIG. 1 also includes sense comb 26 and 32,typically at the opposite end of flexural plate 38 from drive combs 14and 26, with sense teeth 28, 30, and 34, 36, respectively. As discussedabove in the Background section, prior art sensor 10 relies on a theorybased on surface acoustic waves (SAW) wherein waves propagate away fromdrive combs 14 and 20 toward sense combs 26 and 32, as indicated byarrow 50, FIG. 4, and back reflections are regarded as interference.Reliance on SAW theory, however, does not account for numerous smallpeaks produced by sensor 10, results in calculated gains which are low,and cannot account for sharp phase drops.

In contrast, flexural plate wave sensor 70, FIG. 5 of the subjectinvention includes flexural plate 72 having a length and a width, andcomb pattern 74 over flexural plate 72 with drive teeth 76 disposedacross the entire length of flexural plate 72 to reduce the number ofeigenmodes excited in plate 72. In one design, comb pattern 74 isaligned with all the eigenmodes of flexural plate 72. In a preferredembodiment, only one eigenmode is excited. The result is that flexuralplate wave sensor 70 outputs a single pronounced peak, e.g., peak 80,FIG. 6A, with a distinct phase, as shown in FIG. 6B, or a pronouncedpeak much larger than any of the other peaks, e.g., peak 82, FIG. 7A,compared to peaks 84, and 86, with a distinct phase, as indicated byarrow 89, FIG. 7B. This is in stark contrast to the peaks of similaramplitude and irregular phase produced by prior art sensors, as shown inFIGS. 3A and 3B. The result is a significant simplification in theoperation and design of flexural plate wave sensor 70, FIG. 5. With onlya single mode capable of being excited, the design of closed loopelectronics of this invention, discussed below, improves stability ofthe system because erroneous readings do to interference created by modehopping from other eigenmodes (as shown in FIGS. 3A and 3B) is notpossible.

In one design in accordance with this invention, sensor 70 furtherincludes sense teeth 78 disposed across the entire length of flexuralplate 72. In one embodiment, sense teeth 78 and drive teeth 76 face inopposite directions. In this design, sense teeth 78 are interleaved withdrive teeth 76. Sense teeth 78 are typically aligned with the eigenmodesexcited in flexural plate 72 to detect the output produced by driveteeth 76.

In one example of this invention, comb pattern 74 is made of copper. Inother examples, comb pattern 74 is made of titanium-platinum-gold(TiPtAu), titanium-platinum (TiPt), aluminum, or any known materials orcombination of materials known to those skilled in the art. Typically,comb pattern 74 is approximately 0.1 μm thick and includes wire bond padareas 80, and 82, FIG. 5.

Flexural plate wave sensor 70 is typically comprised of several layersas shown in FIG. 8. Sensor 70 may include base substrate 100, typicallya silicon substrate 380 μm thick and etch stop layer 102, ideally 1 μmthick and made of silicon-oxide (SiO₂) disposed over base substrate 100.Ideally, sensor 70 also includes membrane layer 104, typically made ofsilicon or similar material and is disposed over etch stop layer 102 andcavity 106. Additional silicon is typically grown to form membrane layer104 (e.g., diaphragm layer). Cavity 106 has substantially parallelinterior walls and is disposed within base substrate 100 and etch stoplayer 102 thereby exposing a portion of membrane layer 104. In oneexample, piezoelectric layer 108 with a thickness of 0.5 μm is disposedon membrane layer 104. Comb pattern 74 with drive teeth 76 and senseteeth 78 (as also shown in FIG. 5) is disposed over piezoelectric layer108. Typically, layer 104 is connected to ground (not shown).Piezoelectric layer 108 is ideally formed from a material such asaluminum nitride, zinc oxide, and lead zirconium titanate.

In other designs, base substrate 100 is a silicon-on-insulator (SOIwafer) and includes upper surface of silicon (e.g., membrane 104) bondedto etch stop layer 102. Ideally, grounding contacts to silicon layer(e.g., membrane 104) are provided by etching an opening intopiezoelectric layer 108. In one preferred example,titanium-platinum-gold metal or titanium-platinum is patterned to definecomb pattern 74, FIG. 5 with drive teeth 76 and sense teeth 78 disposedacross the entire length of piezoelectric layer 108, FIG. 8. Ideally,comb pattern 74 further defines wire bond pad areas 80 and 82, FIG. 5and grounding contacts (not shown). Typically, drive teeth 76 and senseteeth 78 are 300 μm to 2000 μm in length and the spacing between thedrive and sense teeth is approximately 25 to 50 μm.

As shown above, the unique design of comb pattern 74 of flexural platewave sensor 70 with drive teeth 76 disposed across the entire length offlexural plate 72 effectively reduces the number of eigenmodes excitedin the flexural plate and outputs a single pronounced peak, or a peakmuch larger than any of the other peaks output by sensor 70. The resultis a simplification in the operation and design of flexural wave platesensor 70.

Unique comb pattern 74 may take several forms including sets ofinterleaved drive teeth and interleaved sense teeth which each span theentire length and approximately fifty percent of the width of theflexural plate (FIG. 9), two sets of interleaved drive and sense teethwherein each set of interleaved drive and sense teeth spans the entirelength and approximately fifty percent of the width of the flexuralplate (FIG. 10), two sets of interleaved drive and sense teeth whereinone set of interleaved drive and sense teeth spans approximatelyseventy-five percent of the length of the flexural plate and the otherset spans approximately twenty-five percent of the flexural plate (FIG.11), and unique curved sets of drive and sense teeth (FIG. 12). Otherequivalent embodiments may occur to those skilled in the art.

Comb pattern 74′, FIG. 9 includes first set 120 of drive teeth andsecond set 124 of drive teeth disposed across the entire length offlexural plate 72. Comb pattern 74′ may also include first set 128 ofsense teeth and second set 130 of sense teeth also disposed across theentire length of flexural plate 72 and are used to sense the outputprovided by first set 120 and second set 124 of drive teeth. In oneexample, first set 120 of drive teeth is driven at a negative polarityand second set 124 of drive teeth is driven at a positive polarity toalign with the negative and positive peaks of the eigenmodes of flexuralplate 72 and aid in the reduction of eigenmodes excited. Similarly,first set 128 of sense teeth is driven at a positive polarity and secondset 130 of sense teeth is driven at a negative polarity. First set 120and second set 124 of drive teeth may face in opposite directions andare interleaved with each other. Similarly, first set 128 and second set130 of sense teeth face in opposite directions and are interleaved witheach other. In this design, first set 120 of drive teeth is interleavedwith second set 124 drive teeth which together are disposed across theentire length of flexural plate 72 and span approximately 50 percent ofthe width of flexural plate 72. Similarly, first set 128 of sense teethis interleaved with second set 130 of sense teeth which together aredisposed across the entire length of flexural plate 72 and span theremaining 50 percent of the width of flexural plate 72. The design ofcomb pattern 74′ not only reduces the number of eigenmodes excited butalso helps reduce the number of peaks output by sensor 70′.

In another example of this invention, the design of comb pattern 74′described above is modified to interleave the first set of drive teethwith the first set of sense teeth as shown in FIG. 10. Comb pattern 74″includes first set of drive teeth 131 interleaved with first set ofsense teeth 132. Interleaved sets 131 and 132 are disposed across theentire length of flexural plate 72 and fifty percent of the width offlexural plate 72. Comb pattern 74″ also includes second set of driveteeth 134 interleaved with second set of sense teeth 136, whichsimilarly span the entire length of flexural plate 72 and fifty percentof the width of flexural plate 72. Typically the sets of drive teeth(e.g., sets 131 and 134) and the sets of sense teeth (e.g., sets 132 and136) are driven at opposite polarities. Similar to the above design inFIG. 9, this design not only reduces the number of eigenmodes excitedbut also reduces the number of peaks produced by sensor 70.

In yet another design, comb pattern 74′″, FIG. 11A includes first set150 of drive teeth and second set 152 of drive teeth. First set 150spans approximately 75 percent of flexural plate 72 and second set 152spans approximately 25 percent the length of flexural plate 72. Combpattern 74′″ may further include first set 154 of sense teeth whichspans approximately 75 percent of the length of flexural plate 72 and isinterleaved with first set 150 of drive teeth. Comb pattern 74′″ mayalso include second set 154 of sense teeth which span approximately 25percent of the length of flexural plate 72 and is interleaved withsecond set 152 of drive teeth. This design also reduces the number ofeigenmodes excited in flexural plate 72.

In one embodiment, comb pattern 74 ^(iv), FIG. 11B may include driveteeth 170 and sense teeth 172 disposed over flexural plate 72. Driveteeth 170 span approximately fifty percent of length of the flexuralplate 72, as indicated by arrow 174, and sense teeth 172 spanapproximately fifty percent of the length of flexural plate 72, asindicated by arrow 176. Comb pattern 74 ^(iv) similarly reduces thenumber of eigenmodes excited in flexure plate 72.

In another design, comb pattern 74 ^(iv) may include set of drive teeth173 which includes drive teeth 170 and drive teeth 171. Set of driveteeth set 173 spans approximately fifty percent of the length offlexural plate 72, similarly indicated by arrow 174. Comb pattern 74^(iv) also includes set of sense teeth 175 which includes sense teeth172 and sense teeth 177. Set of sense teeth set 175 spans approximatelyfifty percent of the length of flexural plate 72, as indicated by arrow176. This design also reduces the number of eigenmodes excited inflexural plate 72. Although as shown in FIG. 11B, set of drive teeth 173includes drive teeth 170 interleaved with drive teeth 171 and set ofsense teeth 175 includes sense teeth 172 interleaved with sense teeth177, this is not a necessary limitation of this invention, as driveteeth (e.g., drive teeth 170 or drive teeth 171) may also be interleavedwith the sense teeth (e.g., sense teeth 172 or 177).

In another design in accordance with this invention, comb pattern 74^(v), FIG. 12 includes first set 160 of drive teeth and second set 162of drive teeth disposed across approximately 50 percent of the length offlexural plate 74. First set 160 and second set 162 of drive teeth spanapproximately the entire width of flexural plate 74 at one end and curvedownward towards center 164 of flexural plate 74. The unique design ofcomb pattern 74 ^(v) helps reduce the number of eigenmodes excited inthe plate and also aids in reducing the number of peaks output by sensor70. Comb pattern 74 ^(v) may also include first set 166 of sense teethinterleaved with second set 168 of sense teeth of similar configurationto first and second sets 160, and 162 of drive teeth as described above.

The method for manufacturing the flexural plate wave sensor 70 of thisinvention includes the steps of: depositing an etch top layer 102, FIG.8 over substrate 100, step 200, FIG. 13; depositing (e.g., growingadditional silicon) membrane layer 104, FIG. 8 over etch top layer 102,step 202, FIG. 13; depositing piezoelectric layer 108, FIG. 8 overmembrane layer 104, step 204, FIG. 13; forming comb pattern 74, FIG. 8(and FIGS. 5, and 9-11) on piezoelectric layer 108 with drive teeth 76which span across the entire length, or portion thereof, ofpiezoelectric layer 108, step 206, FIG. 13; and etching cavity 106, FIG.8 through substrate 100 between cavity 106 and membrane layer 104 toexpose a portion of membrane layer 104, step 208, FIG. 13. In otherexamples, a silicon-on-insulator wafer (SOI) is employed which includesthe oxide layer (e.g., etch stop layer 102) and the silicon diaphragmlayer (e.g., membrane layer 104) already bonded together.

As shown above, the robust flexural plate wave sensor of the subjectinvention includes a comb pattern of several unique configurations whichis disposed across the entire length of the flexural wave plate andreduces the number of eigenmodes excited in the plate thereby providingfor a simple operation and design of the flexural wave plate. The uniquecomb pattern with drive teeth that span the entire length of theflexural wave plate provides the ability for the comb pattern to bealigned with the eigenmodes of the flexural wave plate. The result isthe ability for flexural plate wave sensor 70 to produce a singlepronounced peak, or a peak much larger than any of the other peaks, andprovide greater stability, improved performance, and simplification ofthe design of the flexural plate wave sensor.

As stated in the Background section above, prior art sensor 10, FIG. 1utilizes drive combs 14 and 20 and sense combs 26 and 32 at oppositeends of the flexural plate. Prior art sensor 10 relies on theory basedon an analogy to surface acoustic waves (SAW) wherein the wavespropagate away from the drive combs 14 and 20 toward the sense combs 26and 32, as shown in FIG. 4, and back reflections are regarded asinterference.

The inventors hereof realized that such an analogy to SAW was incorrectfor most flexural plate wave devices. In particular, design with simpleedge conditions, such as the flexural plate shown in FIG. 14 and FIGS.9-11, actually behaves as a resonating plate. The analysis below,equations (1) through (14), is based on modeling flexural plate 302,FIG. 14 as a thin beam. Comparisons to product performance andcalculations of flexural plate 302 eigenfrequencies indicate that thebeam model is valid for resonating plate 302 and sensor 300, as well assensor 70 as shown in FIGS. 5 and 9-11. Equations (16) and (17) belowaugment the simple beam model to consider additional modes across theflexured plate 302 thickness.

As shown in FIG. 14, the drive voltage of flexural wave plate sensor300, which includes flexural plate 302, is referenced to zero andapplied to center grounded transformer 304 which applies +V_(D) to oneelectrode and −V_(D) to the other. The input side of the transformer 304is connected to ground 306 and V_(D). The output side is center tappedso that the ends are +V_(D) and −V_(D). In another example of thisinvention, one port operation may be employed using the drive circuit asan output, such as with a Pierce or series oscillator as known to thoseskilled in the art. A drive pair consists of two electrodes, e.g.,electrodes or drive combs 350 and 352 at +V_(D) and −V_(D). A sense pairmay consist of two electrodes or sense combs, e.g., electrodes or sensecombs 354 and 356, which are typically connected to the inputs ofdifferential amplifiers, such as differential amplifiers 355 and 357,respectively. In one design, all the electrodes, e.g., electrodes orcombs 350, 352, 354 and 356 are deposited on top of the piezoelectriclayer (not shown) of flexural plate 302. (Similar to the design offlexural plate 70, FIG. 8 discussed above.) Silicone layer 309, FIG. 14is typically connected to ground 306.

The relationship between the eigenmodes and flexural plate voltage isshown below. The derivation of equation (1) below is disclosed in“Modeling Flexural Plate Wave Devices”, Weinberg et al., Journal ofMicroelectro Mechanical Systems, Vol. 9, (September 2000), incorporatedherein by reference. The following equations are based on a thin beamvibrating in the z direction as shown in FIG. 14. The displacement atany position is given by: $\begin{matrix}{{z(t)} = {\sum\limits_{n = 1}^{\infty}{{A_{n}(t)}{\varphi_{n}(x)}}}} & (1)\end{matrix}$The equation of motion for each mechanical mode is: $\begin{matrix}{{{m_{p}{\overset{¨}{A}}_{n}} + {b{\overset{.}{A}}_{n}} + {m\quad\omega_{n}^{2}A_{n}}} = {\frac{\int_{0}^{\ell}{{\varphi_{m}(x)}{f\left( {x,t} \right)}{\mathbb{d}x}}}{\int_{0}^{\ell}{{\varphi_{n}^{2}(x)}{\mathbb{d}x}}} = {f_{n}(t)}}} & (2)\end{matrix}$where${\phi_{n}(x)} \approx {\sin\quad\left( {{\lambda_{n}x} - \frac{\pi}{4}} \right)}$=eigenmode shape for built-in diaphragm edges, which equals sin(λ_(n)x)for simple supports, $\lambda_{n} = {\frac{{2n} + 1}{2L}\pi}$equals eigenvalue for built-in edges, and λ_(n)=nπ is the eigenvalue forsimply supported edges. Further, where n is a positive integer equal tothe number of half wavelengths in length L, m_(p) is the mass per unitlength, b is the damping per unit length, A_(n) is the amplitude ofmotion of the excited n'th mode, L is flexural plate length, andf_(n)(t) is the forcing function for mode n.

For simple and built-in supports, the angular resonant frequency isrelated to the wave number λ by: $\begin{matrix}{\omega_{n} = {\sqrt{\frac{D}{m}}\lambda_{n}^{2}}} & (3)\end{matrix}$where D is the rigidity.

Assuming the mode shape is given by: $\begin{matrix}{{\varphi_{n}(x)} = {\sin\quad\left( {\frac{n\quad\pi\quad x}{\ell} - \varphi} \right)}} & (4)\end{matrix}$Also assume pinned beams for which φ=0. Because of the large number ofmodes, pinned and built-in beams differ little. Assume also that thebeam is driven by a force density whose first harmonic is:$\begin{matrix}{{w\left( {x,t} \right)} = {w_{a}\sin\quad\left( {\frac{2\quad\pi\quad x}{P} - \theta} \right)\quad\sin\quad\left( {\omega\quad t} \right)}} & (5)\end{matrix}$where${w_{a} = {{- \frac{2\sqrt{2}}{\pi}}\left( \frac{m\quad\pi}{\ell_{t}} \right)^{2}M_{p}V_{D}}},M_{p}$is the magnitude of piezoelectric torque per volt applied to electrodes,V_(D) is the voltage applied to drive teeth 352, θ is the alignmentbetween comb fingers and reference, l_(t) is length of transducer whichequals mP/2, P is the comb pitch, and m is number of combs in transduceror the number of half sines in L_(t).

With equations (2), (4) and (5), the modal forcing function isdetermined from: $\begin{matrix}{{f_{n}(t)} = {w_{a}\quad\sin\quad\left( {\omega\quad t} \right)\frac{2}{\ell}{\int_{x_{o}}^{x_{o} + \ell_{t}}{\sin\quad\left( {\frac{n\quad\pi\quad x}{\ell} - \varphi} \right)\quad\sin\quad\left( {\frac{m\quad\pi\quad x}{\ell_{t}} - \theta} \right){\mathbb{d}x}}}}} & (6)\end{matrix}$where the comb starts at x_(o) and ends at x_(o)+l_(t). From equation(6) γ_(n) is defined and relates the modal force to the input voltage:$\begin{matrix}\begin{matrix}{\frac{f_{n}}{V_{D}} = {k_{n}\gamma_{n}}} \\{= {{- \frac{2\sqrt{2}}{\pi}}\left( \frac{m\quad\pi}{\ell_{t}} \right)^{2}M_{p}\quad\sin\quad\left( {\omega\quad t} \right)\frac{2}{\ell}{\int_{x_{o}}^{x_{o} + \ell_{t}}{\sin\quad\left( {\frac{n\quad\pi\quad x}{\ell} - \varphi} \right)}}}} \\{\sin\quad\left( {\frac{m\quad\pi\quad x}{\ell_{t}} - \theta} \right){\mathbb{d}x}}\end{matrix} & (7)\end{matrix}$Equation (7) applies to both the comb and sense electrodes, e.g., combpattern 350 with drive teeth 350 and 352, and sense teeth 354 and 356(or any of the designs shown in FIGS. 5 and 9-12). The integral is takenover the transducer length l_(t) as shown in FIG. 11, since the combsexert the force. With simple support, φ is equal to 0. The units of γare m/V and γ is proportional to 1/λ_(n) ⁴. When the combs and modes arealigned, θ is equal to 0 and the forcing function is: $\begin{matrix}{{f_{n}(t)} = {w_{a}\quad{\sin\left( {\omega\quad t} \right)}\frac{l_{t}}{l}\left\{ {\frac{\sin\left\lbrack {\left( {\frac{l_{t}n}{l} - m} \right)\quad\pi} \right\rbrack}{\left( {\frac{l_{t}n}{l} - m} \right)\quad\pi} - \frac{\sin\left\lbrack {\left( {\frac{l_{t}n}{l} + m} \right)\quad\pi} \right\rbrack}{\left( {\frac{l_{t}n}{l} + m} \right)\quad\pi}} \right\}}} & (8)\end{matrix}$

The model amplitudes responses f_(n)(t)/[W_(a) sin(ωt)] for phase θ ofzero, π/4, and π/2 are shown in FIGS. 15A-15C with a transducer lengthof 0.00125 meters, flexural plate 302, FIG. 14 a length of 0.005 meters,and m equals 50, yielding a 50 μm pitch. When the wavelength of theeigenmode matches the comb pitch, the maximum forcing of flexural platewave sensor 300 is achieved.

In accordance with this invention, when the drive length, e.g., thelength of comb pattern 300 with drive teeth 352 (or the designs shown inFIGS. 5 and 9-11) disposed across the entire length of flexural plate302, only one mode in the x direction is excited and the responsebecomes a simple second order system, producing a single pronouncedpeak, as shown in FIG. 6A. Moreover, by varying the comb length andtooth width it is possible to trim the piezoelectric bending as afunction of γ which can force harmonics so that the y direction sinusoidharmonics are not excited.

In equation (8), the force per length w(x,t) was represented by itsfirst harmonic. The modal forcing function f_(n)(t) in equation (6) isdominated by terms with denominators which include$\left( {\frac{l_{t}n}{l} - m} \right);$thus, higher harmonics of w(x,t) have larger values of m and contributelittle to equation (8).

Coupling of beam modes into output utilizes the conversion of straininto charge on the flexural plate 302, FIG. 14. Assuming flexural plate302 is grounded, the surface charge per unit length is described by:Q _(x) =d ₃₁ Ybε _(p)(1+ν_(P)) (9)where d₃₁ is the piezoelectric constant relating z electric field to xstrain, Y is Young's modulus of the piezoelectric material, ν_(p) isPoisson's ratio and b is the width of diaphragm.

Using equations (1) and (4), the peak x strain at area center forpiezoelectric material, ε_(p), is related to the modal amplitudes by:$\begin{matrix}{ɛ_{p} = {\frac{\Delta\quad z_{m}}{R} = {{\frac{\partial^{2}z}{\partial x^{2}}\Delta\quad z_{m}} = {- {\sum{\left( \frac{n\quad\pi}{l} \right)^{2}\quad\Delta\quad y_{m}{A_{n}(t)}\quad{\sin\left( {\frac{n\quad\pi\quad x}{l} - \varphi} \right)}}}}}}} & (10)\end{matrix}$where ΔZ_(m) is the distance between the piezoelectric material's centerof area and the flexural plate's neutral axis for torque inputs, andR=radius of curvature at position.

The total charge is calculated by integrating equation (9) over theelectrodes (e.g., comb patterns 350 and 352, FIG. 14). Because of thesine function in equation (10), this integration is similar to a Fouriertransform so that is easier to consider the first harmonics of the platedistribution: $\begin{matrix}{Q = {{\int_{electrodes}^{\quad}{Q_{x}{\mathbb{d}x}}} \approx {\frac{2\sqrt{2}}{\pi}\quad{\int_{x_{o}}^{x_{o} + l_{t}}{Q_{x}\quad{\sin\left( {\frac{m\quad\pi\quad x}{l_{t}} - \theta} \right)}{\mathbb{d}x}}}}}} & (11)\end{matrix}$

With equations (9) and (10) inserted into equation (11), the totalcharge on the sense or drive electrodes (e.g., drive teeth 350 and 352or sense teeth 354 and 356) is: $\begin{matrix}{Q = {\sum\limits_{n}{\alpha_{n}A_{n}}}} & (12)\end{matrix}$where the coupling between modal amplitude and charge is given by:$\begin{matrix}{\alpha_{n} = {{- \left( \frac{n\quad\pi}{l} \right)^{2}}d_{31}\quad{Yb}\quad\Delta\quad z_{m}\quad{\frac{l\sqrt{2}}{\pi}\left\lbrack {\frac{2}{l}{\int_{x_{o}}^{x_{o} + l_{t}}{{\sin\left( {\frac{n\quad\pi\quad x}{l} - \varphi} \right)}\quad{\sin\left( {\frac{m\quad\pi\quad x}{l_{t}} - \theta} \right)}{\mathbb{d}x}}}} \right\rbrack}}} & (13)\end{matrix}$

The integral in brackets is identical to that used to calculate themodal force of equation (7). The units of α_(n) are Coul/m and α_(n) isproportional to λ_(n) ².

Insert the piezoelectric diaphragm model into a lumped parameter modelwith other electrical circuit elements as follows. The piezoelectriccomb pair, for example 349, typically includes two electrodes, e.g., 350and 352, and ground plane 306. For a single mode, the static equationrelating modal displacement and charge to electrode voltage and modalforce is: $\begin{matrix}{{\begin{bmatrix}1 & 0 & {- \frac{\alpha_{n}}{2}} \\0 & 1 & \frac{\alpha_{n}}{2} \\0 & 0 & 1\end{bmatrix}\begin{bmatrix}Q_{D1} \\Q_{D2} \\A_{n}\end{bmatrix}} = {\begin{bmatrix}{C + C_{12}} & {- C_{12}} & 0 \\{- C_{12}} & {C + C_{12}} & 0 \\\frac{\gamma_{n}}{2} & {- \frac{\gamma_{n}}{2}} & \frac{1}{k_{n}}\end{bmatrix}\begin{bmatrix}V_{D1} \\V_{D2} \\f_{n}\end{bmatrix}}} & (14)\end{matrix}$where C is capacitance from one plate to ground, C₁₂ is capacitancebetween positive and negative electrodes, α_(n), γ_(n) are piezoelectriccoupling coefficients defined in equations (7) and (13), k_(n)=modalstiffness, D₁ refers to a positive drive electrode, e.g., drive teeth350, and D₂ refers to a negative drive electrode 352. The negative signson α_(n) and γ_(n) indicate that the negative electrodes are displaced180 degrees from the positive electrodes. The voltage applied to thenegative comb is minus that applied to the plus electrodes:V _(D) =V _(D1) =−V _(D2)  (15)

With small coupling assumption implicit in equation (14), the voltagesand currents applied to flexural plate plates are still described byequations (9) through (13). Equation (14) formulation results inQ_(D2)=−Q_(D1) which is consistent with the circuit diagram of FIG. 14.Q_(D1) is the integral of the current I₂ defined above. Symmetry anddifferential read out define:Q=Q _(D1) −Q _(D2)  (16)

Equation (16) is simplified to: $\begin{matrix}{{\begin{bmatrix}1 & {- \alpha_{n}} \\0 & 1\end{bmatrix}\begin{bmatrix}Q \\A_{n}\end{bmatrix}} = {\begin{bmatrix}{2\left( {C + {2C_{12}}} \right)} & 0 \\\gamma_{n} & \frac{1}{k_{n}}\end{bmatrix}\begin{bmatrix}V_{D} \\f_{n}\end{bmatrix}}} & (17)\end{matrix}$

When adding the circuit resistors, the Q consists of two currents asoutlined in equation (16). Equations (16) and (17) describe both thedrive and sense electrode pairs.

The charge is the total charge summed over the electrode while the forceis the modal force which is a force per unit length along the beam. Whenthe mode period matches the combs' period: $\begin{matrix}{\lambda_{n} = {\frac{n\quad\pi}{l} = \frac{m\quad\pi}{l_{t}}}} & (18)\end{matrix}$and the combs are aligned with the eigenmode [θ equals φ in equation 7],the piezoelectric equation (17) obeys a form of reciprocity as shown by:$\begin{matrix}{{\gamma_{n}k_{n}} = \frac{2\quad\alpha_{n}}{l}} & (19)\end{matrix}$The reciprocity demonstrates a symmetry between voltage, modal force,charge per length, and modal amplitude. When the eigenmodes are notaligned with the combs, equation (19) does not govern.

The results of the above are combined into a comprehensive dynamicflexural plate wave sensor of this invention which relates excitationvoltage to the preamplifier output. For clarity, only 3 modes areincluded in this example. However, this is not a necessary limitation ofthis invention, as any number of modes may be included by those skilledin the art and shown in FIGS. 3A, 3B, 6A, 6B, 7A and 7B. As statedabove, the charge includes both the plus and minus plates. The voltageand force applied directly to the piezoelectric material are shown as:$\begin{matrix}{\begin{bmatrix}1 & 0 & {- \alpha_{D\quad 1}} & {- \alpha_{D\quad 2}} & {- \alpha_{D\quad 3}} \\0 & 1 & {- \alpha_{S\quad 1}} & {- \alpha_{S\quad 2}} & {- \alpha_{S3}} \\0 & 0 & k_{1} & 0 & 0 \\0 & 0 & 0 & k_{2} & 0 \\0 & 0 & 0 & 0 & k_{3}\end{bmatrix}{\quad{\begin{bmatrix}Q_{D} \\Q_{S} \\A_{1} \\A_{2} \\A_{3}\end{bmatrix} = {\begin{bmatrix}C_{D} & 0 & 0 & 0 & 0 \\0 & C_{S} & 0 & 0 & 0 \\{k_{1}\gamma_{D\quad 1}} & {k_{1}\gamma_{S\quad 1}} & 1 & 0 & 0 \\{k_{2}\gamma_{D\quad 2}} & {k_{2}\gamma_{S\quad 2}} & 0 & 1 & 0 \\{k_{3}\gamma_{D\quad 3}} & {k_{3}\gamma_{S\quad 3}} & 0 & 0 & 1\end{bmatrix}\begin{bmatrix}V_{D} \\V_{S} \\f_{1} \\f_{2} \\f_{3}\end{bmatrix}}}}} & (20)\end{matrix}$The force applied to the piezoelectric material is described by.f _(n) =−b _(n) {dot over (A)} _(n) −m _(p) Ä _(n)  (21)The voltage applied to the drive comb 350, FIG. 14 is:V _(D) =V−sQ _(D) R _(D)  (22)where V=voltage applied by the source and R_(D) is the input resistor.

Assuming that the output preamplifier is at virtual ground, the sensevoltage is given by: $\begin{matrix}{V_{s} = {{- {sQ}_{s}}\frac{R_{s}}{2}}} & (23)\end{matrix}$where R_(S) is the sense resistor. The factor of two accounts for thedefinition of Q of equation (15) which includes both the positive andnegative electrodes. The MATLAB® code for equations (20) through (23) toobtain frequency responses is shown in FIGS. 16A-16C.

As a first approximation for a rectangular plate, e.g., flexural plate302, FIG. 14 the eigenmodes in the x and γ directions are close to thosederived from beam theory as shown by J. Blevins, Formulas for NaturalFrequency and Mode Shape, Robert E. Krieger Publishing Co., Malabar,Fla. (1979). The displacement is a sinusoid in x multiplied by asinusoid in y. For an isotropic or orthotropic rectangular platebuilt-in or simply supported on four edges, the eigenfrequencies (in Hz)are given approximately by: $\begin{matrix}{f_{nm} = {\frac{\pi}{2}\sqrt{\frac{{G(n)}^{4}}{\ell^{4}} + \frac{{G(m)}^{4}}{b^{4}} + \frac{2{J(n)}{J(m)}}{\ell^{2}b^{2}}}\sqrt{\frac{{Yh}^{3}}{12{m_{a}\left( {1 - v^{2}} \right)}}}}} & (24)\end{matrix}$where n is the mode number along length, m is the mode number acrosswidth, l=length of plate, in one example 0.005 m, b is the width ofplate, such as 0.001 m, G(n) equals n for simple supports and n+½ forall edges built-in, J(n)=n² for simple support and is equal to$\left( {n + \frac{1}{2}} \right)^{2}\left\lbrack {1 - \frac{2}{\pi\left( {n + \frac{1}{2}} \right)}} \right\rbrack$with all edges built-in, Y is Young's modulus, h is the plate thicknessand m_(a)=mass per unit area.

For a simply supported plate, equation (24) becomes: $\begin{matrix}{f_{nm} = {\frac{\pi}{2}\sqrt{\frac{{Yh}^{3}}{12{m_{a}\left( {1 - v^{2}} \right)}}}\left( {\frac{n^{2}}{\ell^{2}} + \frac{m^{2}}{b^{2}}} \right)}} & (25)\end{matrix}$

For the nominal case, the eigenfrequencies relative to m=0 and simplesupport are plotted versus m in FIG. 17. For l/b=5. Equations (24) and(25) duplicates beam theory when m=0. The built-in eigenfrequency is0.50% higher than the simple support. With m=1 and n=200, the built-in'sresonant frequency is 0.085% larger than the m=0 simple beam case. Thism=1 frequency is near the beam theory value and is the basic operatingfrequency. As shown in FIG. 18, displacements are close to the m=1 modeshape. Higher m modes are more half sines in the y (short) direction.With m=2, the next resonance is 0.21% above the basic operatingfrequency (m=1). With straight teeth, the excitation is an odd harmonicand should not be excited (except for fabrication deviations). Forbuilt-ins, the m=3 resonance is 0.6% higher than the fundamental.Although the excitation is square in the y direction, the response alonga fixed x is largely sinusoidal as shown in FIG. 18. With square drivethe third harmonic of the drive is ⅓ the fundamental. FIG. 3A shows araggedness associated with prior art sensor 10 which crosses modes. Insharp contrast, flexural wave plate sensor 70, FIGS. 5, 9-11 and sensor300, FIG. 14 in accordance with this invention, include the unique combpattern which extends across the entire length of the flexural platethat produces simple pronounced peaks or peaks much larger than anyother peaks as shown in FIGS. 6A and 6B with a distinct phase as shownin FIGS. 7A and 7B.

Although specific features of the invention are shown in some drawingsand not in others, this is for convenience only as each feature may becombined with any or all of the other features in accordance with theinvention. The words “including”, “comprising”, “having”, and “with” asused herein are to be interpreted broadly and comprehensively and arenot limited to any physical interconnection. Moreover, any embodimentsdisclosed in the subject application are not to be taken as the onlypossible embodiments.

Other embodiments will occur to those skilled in the art and are withinthe following claims:

1. A method for manufacturing a flexural plate wave sensor, the methodcomprising the steps of: depositing an etch-stop layer over a substrate;depositing a membrane layer over said etch stop layer; depositing apiezoelectric layer over said membrane layer; forming a comb patternwith drive teeth which span across an entire length of the piezoelectriclayer on said piezoelectric layer; etching a cavity through thesubstrate, the cavity having substantially parallel interior walls; andremoving a portion of the etch stop layer between the cavity and themembrane layer to expose a portion of the membrane layer.
 2. The methodof claim 1 further comprising the steps of etching a hole in thepiezoelectric and forming a ground contact on the silicon membranelayer.
 3. A method for manufacturing a flexural plate wave sensor, themethod comprising the steps of: depositing an etch-stop layer over asubstrate; depositing a membrane layer over said etch stop layer;depositing a piezoelectric layer over said membrane layer; forming acomb pattern on said piezoelectric layer, said comb pattern includingdrive and sense teeth which span an entire length of the membrane layer;forming a second transducer on said piezoelectric layer, spaced fromsaid first transducer; etching a cavity through the substrate, thecavity having substantially parallel interior walls; removing theportion of the etch stop layer between the cavity and the membrane layerto expose a portion of the membrane layer; and depositing an absorptivecoating on the exposed portion of the membrane layer.
 4. The method ofclaim 3 further comprising the steps of etching a hole in thepiezoelectric and forming a ground contact on the silicon membranelayer.